Helen, I certainly understand your concern. As far as I can tell and after checking with the Illinois Natural History medical entomologist we do not know of any place that can check ticks for Lyme disease. He suggested contacting Illinois Public Health. However ticks can be identified by sending them in a vial to the U of I plant clinic. check this website for proper submission.
http://plantclinic.cropsci.uiuc.edu/ In the mean time I would follow your health practioners advice or get a second opinion. I hope all turns out ok for you.